Context. Small universe models predicted a cutoff in large-scale power
in the cosmic microwave background (CMB). This was detected by
the Wilkinson Microwave Anisotropy Probe (WMAP).
Several studies have since proposed that the preferred
model of the comoving spatial 3-hypersurface of the Universe
may be a Poincaré dodecahedral space (PDS) rather than
a simply connected, flat space. Both models assume an FLRW metric and are close to flat
with about 30% matter density.

Aims. We study two predictions of the PDS model. (i) For the correct astronomical positioning of the fundamental domain, the spatial two-point cross-correlation function of temperature
fluctuations in the covering space (where the two points
in any pair are on different copies of the surface of last
scattering (SLS)) should have a similar order of magnitude to
the auto-correlation function on a single copy of the SLS.
(ii) Consider a “generalised” PDS model for an arbitrary “twist” phase . The optimal orientation and
identified circle radius for a generalised PDS model found by maximising
relative to in the WMAP maps should yield one of the two twist angles ±36°.

Methods. Comparison of to extends the identified circles method,
using a much larger number of data points. We optimise the ratio of these functions at scales 4.0 h-1 Gpc using a Markov chain Monte Carlo (MCMC) method
over orientation (l, b, θ), circle size α, and twist ϕ.

Results. Both predictions were satisfied: (i) an optimal generalised PDS solution
was found for two different foreground-reduced versions of the WMAP 3-year
all-sky map, both with and without the kp2 galactic contamination mask.
This solution yields a strong cross-correlation between points which
would be distant and only weakly correlated
according to the simply connected hypothesis.
The face centres are {(l,b)}≈ {
(184°, 62°), (305°, 44°),
(46°, 49°), (117°, 20°),
(176°, -4°), (240°, 13°)}
(and their antipodes) to within ≈2°;
(ii) this solution has twist ϕ = (+39 ± 2.5)°, in agreement with the PDS model.
The chance of this occurring in the simply connected model, assuming a uniform distribution , is about 6-9%.

Conclusions. The PDS model now satisfies several different observational constraints.

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